Cruz was born a U.S. citizen because his mother was an American living in Canada. Some constitutional scholars – and Trump – have questioned whether the circumstances of Cruz's birth meet the "natural born citizen" requirement.

A veteran attorney in Houston, Cruz's hometown, has already challenged the senator's eligibility in a federal court, one of several suits brought against Cruz.

At the Jan. 17 debate, Trump suggested Cruz voluntarily submit the question to the court system, saying "there's a big question mark over your head." Trump said he wouldn't sue, but Democrats surely would if Cruz became the Republican nominee for president.

Now that the field of Republican contenders has narrowed to six, each candidate may constitute a threat to the others' vote totals, and therefore a "unique injury," according to Elhauge. Trump would probably need a state election official to speak up for his claim.

Professor Rick Hasen of the University of California at Irvine told NBC News that it would be unlikely that Trump would have standing in a direct case against Cruz, but that he could sue election officials for allowing Cruz on the ballot.

"And certainly if Cruz were excluded from the ballot by a registrar who said Cruz is ineligible, Cruz would have standing to sue over that," Cruz said.